The correct answer is C. 45 hours.
Since sodium-24 has a half-life of 15 hours, this means that after 15 hours, half of the original amount will remain.
If only one-eighth (1/8) of the sodium-24 remains, then 7/8 of the original amount has decayed.
Since each half-life is 15 hours, multiplying 15 by the number of half-lives (x) we get:
(1/2)^x = (7/8)
To solve for x, we take the logarithm of both sides:
log((1/2)^x) = log(7/8)
x*log(1/2) = log(7/8)
x = log(7/8) / log(1/2)
x ≈ 2.80735
Since x represents the number of half-lives, and each half-life is 15 hours, the total time that has passed is approximately:
2.80735 * 15 hours = 42.11025 hours.
Rounding to the nearest hour, this is equal to 42 hours.
Thus, the closest answer is C. 45 hours.
Sodium-24 has a half-life of approximately 15 hours. If only one-eighth of the sodium-24 remains, about how much time has passed?
A. 15 hours
B. 30 hours
C. 45 hours
D. 60 hours
1 answer